Objectives:

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As an IB Learner you need to be reflective and a good communicator. On your own page of your blog you will need to explain each of these important ideas in your own words:

Fundamental counting principle

Multiplication property of factorials

Formula for permutation

Formula for distinguishable permutations

Formula for combination

Classify and identify counting techniques.

Applications of counting (Rubik's Cube and Instant Insanity)

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TYPE OF PROBLEMS YOU WILL NEED TO SOLVE:

Apply the Fundamental Counting Principle.

Simplify expressions involving factorials.

Know the permutation formula.

Evaluate permutations and distinguishable permutations.

Know the combination formula.

Evaluate combinations.

Distinguish among a permutation, a combination, a distinguishable permutation, and the fundamental counting principle.

Answer applied counting questions.

Use the notation involving Rubik's cube

Explain the Instant Insanity problem

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Permutations

Video:
Counting Using Permutations (time: 10:29)
Permutations (time: 10:10)

Reference Topic Links:

Discusses the building of tree diagrams.
http://www.shodor.org/interactivate/discussions/pd8.html

Permutations:
http://www.cut-the-knot.org/do_you_know/permutation.shtml

Permutation patterns:
http://www.blarg.net/~math/permutations.html

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Combinations

Video:
Counting using Combinations (time: 9:56)
Combinations (time: 10:15)


Sophie Germain:
http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Germain.html

Reference Topic Links:

Combinations:
**http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut57_comb.htm**

Another discussion of combinations can be found here:
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut57_comb_ans.htm

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Counting without Counting

Reference Topic Links:

Here is a comparison of permutations and combinations.
**http://www.mathsisfun.com/combinatorics/combinations-permutations.html**

A review of counting principles including the fundamental counting principle, permutations, combinations, and distinguishable permutations.
This is the elementary version:
http://www.mathagonyaunt.co.uk/STATISTICS/ESP/Perms_combs.html

This is a more advanced version:
http://www.richland.cc.il.us/james/lecture/m116/sequences/counting.html

This site shows a table contrasting the basic counting types of problems.
http://www.math.hawaii.edu/~ramsey/Counting.html

This (somewhat advanced) site is very good if you take some time to understand how to use it. By selecting the second object icon (at the top of the page), you go to an index page. From this index you can find information on permutations, combinations, or distinguishable permutations.
http://www.theory.csc.uvic.ca/~cos/root.html

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Rubik's Cube and Instant Insanity

Video:
PHow to Solve Rubik's Cube - Part I (time: 6:32)
How to Solve Rubik's Cube - Part II (time: 5:49)
Instant Insanity Commercial (time: 0.32)

Reference Topic Links:

Online Rubik's Cube:
**http://neil.rashbrook.org/rubik/**

Design your own cube:
**http://www.randelshofer.ch/rubik/patterns.html**

Information on Rubik's Cube:
http://webplaza.pt.lu/public/geohelm/myweb/cubeold.htm

Online Instant Insanity Puzzle:
http://mysite.verizon.net/msmammek/markspuz.html

Rubik's Cube in four dimensional version
http://www.superliminal.com/cube/cube.htm